140 Treffer

We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes \(W^r_p [0,1]^d\) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.

In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hölder or Sobolev spaces. First we discuss optimal deterministic and randornized algorithms. Then we add a new aspect, which has not been covered before on conferences
about (quasi-) Monte Carlo methods: quantum computation. We give a short introduction into this setting and present recent results of the authors on optimal quantum algorithms for summation and integration. We discuss comparisons between the three settings. The most interesting case for Monte
Carlo and quantum integration is that of moderate smoothness \(k\) and large dimension \(d\) which, in fact, occurs in a number of important applied problems. In that case the deterministic exponent is negligible, so the \(n^{-1/2}\) Monte Carlo and the \(n^{-1}\) quantum speedup essentially constitute the entire convergence rate.

We consider the computation of the mean of sequences in the quantum model of computation. We determine the query complexity in the case of sequences which satisfy a \(p\)-summability condition for \(1\le p<2\). This settles a problem left open in Heinrich (2001).

Free form volumes in rational Bézier representation are defined via homogeneous coordinates and two applications are pointed out : generation of solid primitives and curve and surface modelling by the way of volume deformation. Visualization techniques are reviewed, too.

Software development organizations measure their real-world processes, products, and resources to achieve the goal of improving their practices. Accurate and useful measurement relies on explicit models of the real-world processes, products, and resources. These explicit models assist with planning measurement, interpreting data, and assisting developers with their work. However, little work has been done on the joint use of measurem(int and process technologies. We hypothesize that it is possible to integrate measurement and process technologies in a way that supports automation of measurement-based feedback. Automated support for measurementbased feedback means that software developers and maintainers are provided with on-line, detailed information about their work. This type of automated support is expected to help software professionals gain intellectual control over their software projects. The dissertation offers three major contributions. First, an integrated measurement and
process modeling framework was constructed. This framework establishes the necessary foundation for integrating measurement and process technologies in a way that will permit automation. Second, a process-centered software engineering environment was developed to support measurement-based feedback. This system provides personnel with information about the tasks expected of them based on an integrated set of measurement and process views. Third, a set of assumptions and requirements about that system were examined in a controlled experiment. The experiment compared the use of different levels of automation to evaluate the acceptance and effectiveness of measurement-based feedback.

Wireless LANs operating within unlicensed frequency bands require random access schemes such as CSMA/ CA, so that wireless networks from different administrative domains (for example wireless community networks) may co-exist without central coordination, even when they happen to operate on the same radio channel. Yet, it is evident that this Jack of coordination leads to an inevitable loss in efficiency due to contention on the MAC layer. The interesting question is, which efficiency may be gained by adding coordination to existing, unrelated wireless networks, for example by self-organization. In this paper, we present a methodology based on a mathematical programming formulation to determine the
parameters (assignment of stations to access points, signal strengths and channel assignment of both access points and stations) for a scenario of co-existing CSMA/ CA-based wireless networks, such that the contention between these networks is minimized. We demonstrate how it is possible to solve this discrete, non-linear optimization problem exactly for small
problems. For larger scenarios, we present a genetic algorithm specifically tuned for finding near-optimal solutions, and compare its results to theoretical lower bounds. Overall, we provide a benchmark on the minimum contention problem for coordination mechanisms in CSMA/CA-based wireless networks.